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Wittaler [7]
3 years ago
14

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and tes

t 13 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 6​% rate of​ defects, what is the probability that this whole shipment will be​ accepted?
Mathematics
1 answer:
Pavel [41]3 years ago
6 0

Answer:

0.818

Step-by-step explanation:

Since the shipment has a ton of aspirin tablets, we can assume that we pick 13 of them <em>with</em> <em>reposition, </em>because the probability shoudn't change dramatically from the probability of picking without reposition if we do so.

We call D the amount of defective tablets. If we assume that we pick the tablets with reposition, then we obtain that D is a random variable of Binomial distribution with parameters 13 and 0.6 (the probability of picking a defective tablet).

We want D to be at most one. To calculate the probability of that event we add up the probability of D being equal to 0 and the probability of D being equal to one. Since D is binomial, we have

  • P(D = 0) = (1-0.06)^{13} = 0.447
  • P(D = 1) = {13 \choose 1} * 0.06^1 * (1-0.06)^{12} = 13*0.06*0.94^{12} = 0.371

We conclude that

P(D \leq 1) = P(D = 0) + P(D = 1) = 0.447+0.371 = 0.818

Hence, the shipment will be accepted with probability 0.818

<em>I hope this helps you!</em>

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